Graphing Linear Inequalities in Two Variables

Linear Inequalities• A linear inequality in two variables can be

written in any one of these forms: Ax + By < C Ax + By > C Ax + By ≤ C Ax + By ≥ C

• An ordered pair (x, y) is a solution of the linear inequality if the inequality is TRUE when x and y are substituted into the inequality.

Example 1• Which ordered pair is a solution of

5x - 2y ≤ 6?A. (0, -3)B. (5, 5)C. (1, -2)D. (3, 3)

• The boundary line will be a:– Solid line when ≤ and ≥ are used.–Dashed line when < and > are used.

• Graph will be shaded on one side of the boundary line to show the solutions.

Graphing Linear Inequalities

STEPS:1. Graph the boundary line:

≤ and ≥ will use a solid curve. < and > will use a dashed curve.

2. Test a point NOT on the boundary line to determine which side of the line includes the solutions. If your test point is a solution, shade that

side. If your test points is NOT a solution, shade

the opposite side.

Graphing Linear Inequalities

Example 2• Graph the inequality x ≤ 4 in a coordinate

plane.• HINT: – Decide whether to usea solid or dashed line.

• Use (0, 0) as a test point.

• Shade where the solutions will be.

y

x

5

5

-5

-5

Example 3• Graph 3x - 4y > 12 in a coordinate plane.• Sketch the boundary line of the graph.– Find the x- and y-intercepts and

plot them.– Solid or dashed line?

• Use (0, 0) as a test point.

• Shade where the solutions are.

y

x

5

5

-5

-5

Example 4:Using a new Test Point

• Graph y < 2/5x in a coordinate plane.• Sketch the boundary line of the graph.

Find the x- and y-intercept and plot them.• Use the line’s slope

to graph another point.– Solid or dashed line?

• Use a test pointOTHER than theorigin.

• Shade where the solutions are.

y

x

5

5

-5

-5

Example 5:Let’s Try This!

• Graph y ≥ 3x + 1 in a coordinate plane.

y

x

Example 6:You Try

• Graph y + 2x < 4 in a coordinate plane.

y

x

Example 7:You Try

• Graph 2x – 3y ≤ 6 in a coordinate plane.

y

x

Example 8:You Try

• Graph 2y > x in a coordinate plane.

y

x

Homework

• Inequality Worksheet–SHOW WORK! –GRAPH!